Question

ecause of the community property of multiplication. It is true that 3/4×4 = 4×3/4 however these expressions can be calculated in different ways even though the solution will be the same.

Below show two different ways to solve this problem

First show how 3/4×4 can be solved using repeated edition


Then show how 4×3/4 can be so using multiplication and division

Answer 1

Certainly! Let's break down the problem by solving \( \frac{3}{4} \times 4 \) using repeated addition and \( 4 \times \frac{3}{4} \) using multiplication and division.

### Method 1: Solving \( \frac{3}{4} \times 4 \) using Repeated Addition

The expression \( \frac{3}{4} \times 4 \) can be interpreted as taking \( \frac{3}{4} \) four times. This can be expressed as:

\[
\frac{3}{4} + \frac{3}{4} + \frac{3}{4} + \frac{3}{4}
\]

Now, we can calculate this:

1. First, add the first two fractions:
\[
\frac{3}{4} + \frac{3}{4} = \frac{6}{4}
\]

2. Next, add the next \( \frac{3}{4} \):
\[
\frac{6}{4} + \frac{3}{4} = \frac{9}{4}
\]

3. Finally, add the last \( \frac{3}{4} \):
\[
\frac{9}{4} + \frac{3}{4} = \frac{12}{4}
\]

4. Simplifying \( \frac{12}{4} \):
\[
\frac{12}{4} = 3
\]

So, \( \frac{3}{4} \times 4 = 3 \).

### Method 2: Solving \( 4 \times \frac{3}{4} \) using Multiplication and Division

For \( 4 \times \frac{3}{4} \), we can interpret this as multiplying the whole number 4 by the fraction \( \frac{3}{4} \):

1. Multiply:
\[
4 \times \frac{3}{4} = \frac{4 \times 3}{4}
\]
This simplifies to:
\[
\frac{12}{4}
\]

2. Now, divide:
\[
\frac{12}{4} = 3
\]

Therefore, \( 4 \times \frac{3}{4} = 3 \).

### Conclusion

Both methods confirm that:

\[
\frac{3}{4} \times 4 = 3 \quad \text{and} \quad 4 \times \frac{3}{4} = 3
\]

Thus, we see that the two expressions yield the same result, demonstrating the commutative property of multiplication!